"You're right. My mistake. I don't know how I misread your statement. Sorry. I would like to know what you think my way of adding velocities is."
Well it may be correct if you just misread what I said. I had no idea how you were doing but I knew it had to be wrong because I was right.
"It's hard to keep track of what you're saying when I have to guess under what conditions your statements apply. I maintain that acceleration breaks the symmetry and allows both observers to know the proper acceleration. If there is a proper acceleration, then acceleration is not relative."
We're going to be talking past each other forever on this.
All I'm saying is that the initial acceleration and final deceleration are unimportant...they don't even have to occur. It's the turnaround that matters.
"Actually it's at the .25 and .75 of a circuit. My point is that the Twin Paradox survives your inherent requirement of deceleration back to zero velocity relative to the non-traveling twin."
I don't think you agree with me. (And I am right.) The part of the trip that matters is [0.25-0.75.]. During the first 1.4 and last 1/4 of the journey, the circling observer sees time dilation (not speedup) for the stationary observer. Just think of a straight and back trip. All you're doing is stretching it out along the perpendicular so that the overall speed can stay the same.
This point remains: The observers know which of them is accelerated. Acceleration is not relative. They can determine who has been accelerated, then they calculate the same values. Why would they do any differently? Surely, you're not suggesting that they lie to themselves, are you?
*Because* it has no relevance until the situation changes. Theoretically, the fliught bound observer could accelerate off to infinity forever and he always always always sees a time-dilated earth bound twin. The earth observer sees the exact same thing. This symmetry is *never* broken.
So what if both observers note the same time-dilation for his or her twin? Your argument fails to be relevant. One feels the acceleration that is enough to break the symmetry. Without symmetry, relativity of acceleration is falsified.
Let's work a simple example. Alice and Bob are twins. They are capable of observing their surroundings.
Bob and Alice at time zero at the same location, traveling at the same speed.
As our experiment begins, the UA accelerates BoB at 9.8 ms
-2 up. The UA never accelerates Alice.
After time t (absolute time, say based on the time in the iFoR of the starting point), Bob and Alice observe each other.
Alice notes that Bob's velocity has changed relative to hers and that she has not felt an acceleration.
Bob notes that Alice's velocity has changed relative to his and that he has felt an acceleration.
Alice and Bob both conclude that Bob was accelerated and that Alice was not.
Alice and Bob determine that Alice's velocity relative to their starting velocity remains the same.
Alice and Bob determine that Bob's velocity has changed by adding a positive up velocity of v=gt (non-relativistically, of course. The relativistic equation is too cumbersome to type here).
Since they agree on the change in velocity and in the elapsed time, they get the same value for the acceleration.